Let us consider two numbers X=M.2E and Y=N.2F

We can represent the numbers in binary float point as

The ones complement of (1100)2 is (0011)2. Thus the two complement of this number is obtained as (0011)2+(0001)2=(0100)2.

Since the binary digit b-A is the first bit in the representation of the real number, it is called as the most significant bit(MSB) of the number.

For a two’s complement representation, the truncation error is always negative and falls in the range

Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.

According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).

We can represent 5 as

A fixed point representation of numbers allows us to cover a range of numbers, say, xmax-xmin with a resolution

The binary floating point representation commonly used in practice, consists of a mantissa M, which is the fractional part of the number and falls in the range 1/2<M<1, multiplied by the exponential factor 2E, where the exponent E is either a negative or positive integer. Hence a number X is represented as X= M.2E(1/2<M<1).